The motion of charged particles in electromagnetic fields under extremely nonadiabatic conditions is investigated. This is the case, e.g., if the particle passes through a region of vanishing magnetic field, either in space or in time. In fields of axial symmetry, the constancy of the canonical angular momentum lends the tool for this investigation. Strict laws for flux conservation are derived including rapid changes of fields in space and time. Particle injection into cusped geometries is studied and compared to experimental results. Particle motion under magnetic‐field reversal in time is investigated and compared to findings in &thgr;‐pinch experiments under field reversal. A simple self‐consistent model for such a particle motion is developed leading to the automatic formation of anElayer as a consequence of field reversal.